Gradient-Enhanced Kriging (GEK)
Gradient-Enhanced Kriging (GEK) is a surrogate modeling technique used in engineering. A surrogate model (alternatively known as a metamodel, response surface or emulator) is a prediction of the output of an expensive computer code. This prediction is based on a small number of evaluations of the expensive computer code.
Adjoint solvers are now becoming available in a range of Computational Fluid Dynamics (CFD) solvers, such as Fluent, OpenFOAM, SU2 and US3D. Originally developed for optimization, adjoint solvers are now finding more and more use in uncertainty quantification.
An adjoint solver allows one to compute the gradient of the quantity of interest with respect to all design parameters at the cost of one additional solve. This, potentially, leads to a linear speedup: the computational cost of constructing an accurate surrogate decrease, and the resulting computational speedup scales linearly with the number of design parameters.
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